Calculate the Product: 5^5 × 6^5 Power Multiplication

Question

Choose the expression that corresponds to the following:

$5^5\times6^5=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 When we are presented with a multiplication where each factor has the same exponent (N)

00:07 The entire multiplication can be written with the exponent (N)

00:11 We will apply this formula to our exercise

00:22 This is one potential solution, now let's review another possible solution

00:25 In multiplication, the order of factors doesn't matter, therefore the expressions are equal

00:28 We will apply this formula to our exercise

00:36 This is the solution

Step-by-Step Solution

We are given the expression $5^5 \times 6^5$ .
According to the power of a product rule, $(a \times b)^n = a^n \times b^n$ . Therefore, we can rewrite the expression as $(5 \times 6)^5$ or $(6 \times 5)^5$ .

Both expressions $(5 \times 6)^5$ and $(6 \times 5)^5$ are mathematically equivalent. Therefore, the solution to the problem is that answers (a) and (b) are correct.

Answer

Answers (a) and (b) are correct.

Related Subjects

Exponent of a Multiplication

Question Types

Power of a Product: Applying the formula Power of a Product: Inverse formula